Mathematics is the abstract study
of topics such
as quantity (numbers), structure, s
pace, and change.
The word mathematics comes from
the Greek μάθημα (máthēma), which, in the
ancient Greek language, means "that which
is lea...
Mathematics can, broadly
speaking, be subdivided into
the study of
quantity, structure, space, and
change
(i.e. arithmetic...
Babylonian mathematics refers to any mathematics of the
people of Mesopotamia from the days of the
early Sumerians through...
Babylonian mathematics were written using
a sexagesimal (base-60) numeral system. From this derives
the modern day usage o...
The most extensive Egyptian mathematical text is the Rhind
papyrus (sometimes also called the Ahmes Papyrus after its
auth...
Another significant Egyptian mathematical
text is the Moscow papyrus, also from
the Middle Kingdom period, dated to c.
189...
Greek mathematics is thought to have begun with Thales
of Miletus (c. 624–c.546 BC) and Pythagoras of Samos (c.
582–c. 507...
Following a period of stagnation after Ptolemy, the period
between 250 and 350 AD is sometimes referred to as the "Silver
...
Of particular note is the use in Chinese
mathematics of a decimal positional
notation system, the so-called "rod
numerals"...
The high-water mark of Chinese mathematics
occurs in the 13th century (latter part of
the Sung period), with the developme...
The oldest extant mathematical records from India
are the Sulba Sutras (dated variously between the
8th century BC and the...
In the 5th century AD, Aryabhata wrote
the Aryabhatiya, a slim volume, written in
verse, intended to supplement the rules ...
The Islamic Empire established across Persia,
the Middle East, Central Asia, North
Africa, Iberia, and in parts of India i...
In the 9th century, the Persian mathematician Muḥammad ibn Mūsā alKhwārizmī wrote several important books on the Hindu-Ara...
Other achievements of Muslim mathematicians during this
period include the addition of the decimal point notation to
the A...
During the centuries in which
theChinese, Indian and Islamicmathematicians had
been in the ascendancy, Europe had fallen i...
From the 4th to 12th Centuries, European knowledge
and study of arithmetic, geometry, astronomy and
music was limited main...
By the 12th Century, though, Europe, and particularly Italy, was beginning to trade with the
East, and Eastern knowledge g...
Muslim mathematician
and astronomer whose
major works
introduced HinduArabic numeralsand
the concepts
of algebra into
Euro...
Leonardo Pisano Bigollo

(c. 1170 – c. 1250)

Europe’s first great medieval
mathematician was the
Italian Leonardo of Pisa...
Throughout the 19th century
mathematics became increasingly
abstract. In the 19th century lived Carl
Friedrich Gauss (1777...
This century saw the development of the two forms of nonEuclidean geometry, where the parallel postulate of Euclidean
geom...
The 19th century saw the founding of a
number of national mathematical societies:
the London Mathematical Society in
1865,...
The 20th century saw mathematics become a major
profession. Every year, thousands of new Ph.D.s in
mathematics were awarde...
Differential geometry came into its own when Einstein used it in general
relativity. Entire new areas of mathematics such ...
One of the more colorful figures in 20th-century mathematics
was Srinivasa Aiyangar Ramanujan (1887–1920), an
Indian autod...
In 2000, the Clay Mathematics
Institute announced the seven Millennium
Prize Problems, and in 2003 the Poincaré
conjecture...
Mathematics is creative. Mathematics
is exciting and multifaceted.
Mathematics is the future. Without
mathematics, modern ...
Many mathematicians have been expecting
a great rise of the mathematical inventions
in future.A lot assumtions have been t...
Also many expect to create
a formula as to drive rockets
to such a speed which can
even cross the universe.
The army for...
 Many applications of exploring
trigonometric identities have been
done and many more are in
progress.
Also using the kn...
Nasa also expects to create a
telescope as to see more than
distance of 10 billion kilometers!
The flying car i.e. the o...
These kind of
supercomputers can do
calculations in around 12.3
seconds
Which humans can do in
around 1 million years !!...
Childhood And Early Life
Euclid of ‘Alexandria’ was born around 330 B.C, presumably
at Alexandria. Certain Arabian authors...
Works &
Achievements:
He was responsible in connoting Geometrical
knowledge and also wrote the famous Euclid's Elements
an...
Axioms
Euclid stated that axioms were statements that were
just believed to be true, but he realized that by blindly
follo...
Childhood And Early Life
Euler was born on April 15, 1707, in Basel, Switzerland. His father Paul Euler was a
pastor of th...
Contributions To Mathematics
Mathematical Notation
Among his diverse works, the most notable was the introduction of the
c...
Number Theory
Euler proved Fermat's little
theorem, Newton's identities, Fermat's
theorem on sums of two squares, and he a...
LEONHARD EULER TIMELINE
1707:Was born on April 15, in Basel, Switzerland
1723:Received his Master of Philosophy with a the...
Pythagoras

Childhood And
Early Life
Pythagoras was born in the island
of Samos in around 569 BC. His
father, Mnesarchus, ...
Mathematical Concepts
Pythagoras studied properties of numbers and classified them
as even numbers, odd numbers, triangula...
PYTHAGORAS TIMELINE
570 BC:Pythagoras was born in Samos, Greece.
535 BC:He left Samos and travelled to Egypt
when Polycrat...
Early Life
Srinivasa Ramanujan was born at his grandmother’s house in Erode, a small town
located about 400 km towards sou...
Ramanujan-Hardy Number
(1729)
When Ramanujan fell ill, Hardy came to his
residence to visit Ramanujan in a cab with a
numb...
SRINIVASA RAMANUJAN TIMELINE
1887:
Srinivasa Ramanujan was born in Erode on 22 December.
1889:
He contracted small pox and...
Aryabhatta is the first of the great astronomers of the
classical age of India. He was born in Kerala, South
India in 476 ...
Aryabhatta was the first to explain how the Lunar Eclipse and the Solar
Eclipse happened. Aryabhatta also gave close appro...
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
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JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
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JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
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JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
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JOURNEY OF MATHS OVER A PERIOD OF TIME..................................
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DESCRIBES IN DETAIL ANCIENT AGE ,MEDIEVAL AND PRESENT AGE OF MATHS AND ALSO THE FAMOUS MATHEMATICIANS.REALLY AN AMAZING ONE WITH ANIMATED SLIDE DESIGND..............

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JOURNEY OF MATHS OVER A PERIOD OF TIME..................................

  1. 1. Mathematics is the abstract study of topics such as quantity (numbers), structure, s pace, and change.
  2. 2. The word mathematics comes from the Greek μάθημα (máthēma), which, in the ancient Greek language, means "that which is learnt",what one gets to know," hence also "study" and "science", and in modern Greek just "lesson." The word máthēma is derived from μανθάνω (manthano), while the modern Greek equivalent is μαθαίνω (mathaino), both of which mean "to learn.”
  3. 3. Mathematics can, broadly speaking, be subdivided into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geomet ry, andanalysis).
  4. 4. Babylonian mathematics refers to any mathematics of the people of Mesopotamia from the days of the early Sumerians through theHellenistic period almost to the dawn of Christianity.[20] It is named Babylonian mathematics due to the central role of Babylon as a place of study. Later under the Arab Empire, Mesopotamia, especially Baghdad, once again became an important center of study for Islamic mathematics.In contrast to the sparsity of sources in Egyptian mathematics, our knowledge of Babylonian mathematics is derived from more than 400 clay tablets unearthed since the 1850s. Written in Cuneiform script, tablets were inscribed whilst the clay was moist, and baked hard in an oven or by the heat of the sun.
  5. 5. Babylonian mathematics were written using a sexagesimal (base-60) numeral system. From this derives the modern day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 (60 x 6) degrees in a circle, as well as the use of seconds and minutes of arc to denote fractions of a degree. Babylonian advances in mathematics were facilitated by the fact that 60 has many divisors. Also, unlike the Egyptians, Greeks, and Romans, the Babylonians had a true place-value system, where digits written in the left column represented larger values, much as in the decimalsystem. They lacked, however, an equivalent of the decimal point, and so the place value of a symbol often had to be inferred from the context. On the other hand, this "defect" is equivalent to the modern-day usage of floating point arithmetic; moreover, the use of base 60 means that any reciprocal of an integer which is a multiple of divisors of 60 necessarily has a finite expansion to the base 60. (In decimal arithmetic, only reciprocals of multiples of 2 and 5 have finite decimal expansions.) Accordingly, there is a strong argument that arithmetic Old Babylonian style is considerably more sophisticated than that of current usage.
  6. 6. The most extensive Egyptian mathematical text is the Rhind papyrus (sometimes also called the Ahmes Papyrus after its author), dated to c. 1650 BC but likely a copy of an older document from the Middle Kingdom of about 2000-1800 BC. It is an instruction manual for students in arithmetic and geometry. In addition to giving area formulas and methods for multiplication, division and working with unit fractions, it also contains evidence of other mathematical knowledge, including composite and primenumbers; arithmetic, geom etricand harmonic means; and simplistic understandings of both the Sieve of Eratosthenes and perfect number theory (namely, that of the number 6). It also shows how to solve first order linear equations[27] as well as arithmetic and geometric series.
  7. 7. Another significant Egyptian mathematical text is the Moscow papyrus, also from the Middle Kingdom period, dated to c. 1890 BC.[29] It consists of what are today called word problems or story problems, which were apparently intended as entertainment. One problem is considered to be of particular importance because it gives a method for finding the volume of a frustum: "If you are told: A truncated pyramid of 6 for the vertical height by 4 on the base by 2 on the top. You are to square this 4, result 16. You are to double 4, result 8. You are to square 2, result 4. You are to add the 16, the 8, and the 4, result 28. You are to take one third of 6, result 2. You are to take 28 twice, result 56. See, it is 56. You will find it right."
  8. 8. Greek mathematics is thought to have begun with Thales of Miletus (c. 624–c.546 BC) and Pythagoras of Samos (c. 582–c. 507 BC). Although the extent of the influence is disputed, they were probably inspired by Egyptian and Babylonian mathematics. According to legend, Pythagoras traveled to Egypt to learn mathematics, geometry, and astronomy from Egyptian priests.One of the oldest surviving fragments of Euclid's Elements, found at Oxyrhynchusand dated to circa AD 100. The diagram accompanies Book II, Proposition 5.[35]Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. As a result, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. Pythagoras established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The Pythagoreans are credited with the first proof of the Pythagorean theorem,[38] though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers.[39][40]
  9. 9. Following a period of stagnation after Ptolemy, the period between 250 and 350 AD is sometimes referred to as the "Silver Age" of Greek mathematics.[70] During this period, Diophantus made significant advances in algebra, particularly indeterminate analysis, which is also known as "Diophantine analysis".[71] The study of Diophantine equations and Diophantine approximations is a significant area of research to this day. His main work was the Arithmetica, a collection of 150 algebraic problems dealing with exact solutions to determinate and indeterminate equations.[72] TheArithmetica had a significant influence on later mathematicians, such as Pierre de Fermat, who arrived at his famous Last Theorem after trying to generalize a problem he had read in theArithmetica (that of dividing a square into two squares).[73] Diophantus also made significant advances in notation, the Arithmetica being the first instance of algebraic symbolism and syncopation.
  10. 10. Of particular note is the use in Chinese mathematics of a decimal positional notation system, the so-called "rod numerals" in which distinct ciphers were used for numbers between 1 and 10, and additional ciphers for powers of ten.Thus, the number 123 would be written using the symbol for "1", followed by the symbol for "100", then the symbol for "2" followed by the symbol for "10", followed by the symbol for "3". This was the most advanced number system in the world at the time, apparently in use several centuries before the common era and well before the development of the Indian numeral system.
  11. 11. The high-water mark of Chinese mathematics occurs in the 13th century (latter part of the Sung period), with the development of Chinese algebra. The most important text from that period is the Precious Mirror of the Four Elements by Chu Shih-chieh (fl. 12801303), dealing with the solution of simultaneous higher order algebraic equations using a method similar to Horner's method.[79] The Precious Mirror also contains a diagram of Pascal's triangle with coefficients of binomial expansions through the eighth power, though both appear in Chinese works as early as 1100.[81] The Chinese also made use of the complex combinatorial diagram known as the magic square and magic circles, described in ancient times and perfected by Yang Hui (AD 1238–1298).
  12. 12. The oldest extant mathematical records from India are the Sulba Sutras (dated variously between the 8th century BC and the 2nd century AD),[83] appendices to religious texts which give simple rules for constructing altars of various shapes, such as squares, rectangles, parallelograms, and others.As with Egypt, the preoccupation with temple functions points to an origin of mathematics in religious ritual. The Sulba Sutras give methods for constructing a circle with approximately the same area as a given square, which imply several different approximations of the value of π. In addition, they compute the square root of 2 to several decimal places, list Pythagorean triples, and give a statement of the Pythagorean theorem
  13. 13. In the 5th century AD, Aryabhata wrote the Aryabhatiya, a slim volume, written in verse, intended to supplement the rules of calculation used in astronomy and mathematical mensuration, though with no feeling for logic or deductive methodology. Though about half of the entries are wrong, it is in the Aryabhatiya that the decimal place-value system first appears. Several centuries later, the Muslim mathematician Abu Rayhan Biruni described the Aryabhatiya as a "mix of common pebbles and costly crystals".
  14. 14. The Islamic Empire established across Persia, the Middle East, Central Asia, North Africa, Iberia, and in parts of India in the 8th century made significant contributions towards mathematics. Although most Islamic texts on mathematics were written in Arabic, most of them were not written byArabs, since much like the status of Greek in the Hellenistic world, Arabic was used as the written language of nonArab scholars throughout the Islamic world at the time. Persians contributed to the world of Mathematics alongside Arabs.
  15. 15. In the 9th century, the Persian mathematician Muḥammad ibn Mūsā alKhwārizmī wrote several important books on the Hindu-Arabic numerals and on methods for solving equations. His book On the Calculation with Hindu Numerals, written about 825, along with the work of Al-Kindi, were instrumental in spreading Indian mathematics and Indian numerals to the West. The word algorithm is derived from the Latinization of his name, Algoritmi, and the wordalgebra from the title of one of his works, Al-Kitāb al-mukhtaṣar fī hīsāb alğabr wa’l-muqābala . He gave an exhaustive explanation for the algebraic solution of quadratic equations with positive roots, and he was the first to teach algebra in an elementary form and for its own sake. He also discussed the fundamental method of "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. This is the operation which al-Khwārizmī originally described as aljabr.
  16. 16. Other achievements of Muslim mathematicians during this period include the addition of the decimal point notation to the Arabic numerals, the discovery of all the modern trigonometric functionsbesides the sine, al-Kindi's introduction of cryptanalysis and frequency analysis, the development of analytic geometry by Ibn al-Haytham, the beginning of algebraic geometry by Omar Khayyamand the development of an algebraic notation by al-Qalasādī.[114] During the time of the Ottoman Empire and Safavid Empire from the 15th century, the development of Islamic mathematics became stagnant.
  17. 17. During the centuries in which theChinese, Indian and Islamicmathematicians had been in the ascendancy, Europe had fallen into the Dark Ages, in which science, mathematics and almost all intellectual endeavour stagnated. Scholastic scholars only valued studies in the humanities, such as philosophy and literature, and spent much of their energies quarrelling over subtle subjects in metaphysics and theology, such as "How many angels can stand on the point of a needle?"
  18. 18. From the 4th to 12th Centuries, European knowledge and study of arithmetic, geometry, astronomy and music was limited mainly to Boethius’ translations of some of the works of ancient Greek masters such as Nicomachus and Euclid. All trade and calculation was made using the clumsy and inefficient Roman numeral system, and with an abacus based on Greekand Roman models.
  19. 19. By the 12th Century, though, Europe, and particularly Italy, was beginning to trade with the East, and Eastern knowledge gradually began to spread to the West. Robert of Chester translated Al-Khwarizmi's important book on algebra into Latin in the 12th Century, and the complete text of Euclid's “Elements” was translated in various versions by Adelard of Bath, Herman of Carinthia and Gerard of Cremona. The great expansion of trade and commerce in general created a growing practical need for mathematics, and arithmetic entered much more into the lives of common people and was no longer limited to the academic realm. The advent of the printing press in the mid-15th Century also had a huge impact. Numerous books on arithmetic were published for the purpose of teaching business people computational methods for their commercial needs and mathematics gradually began to acquire a more important position in education.
  20. 20. Muslim mathematician and astronomer whose major works introduced HinduArabic numeralsand the concepts of algebra into European mathematics. Latinized versions of his name and of his most famous book title live on in the terms algorithm and al gebra.
  21. 21. Leonardo Pisano Bigollo (c. 1170 – c. 1250) Europe’s first great medieval mathematician was the Italian Leonardo of Pisa, better known by his nicknameFibonacci. Although best known for the so-called Fibonacci Sequence of numbers, perhaps his most important contribution to European mathematics was his role in spreading the use of the Hindu-Arabic numeral system throughout Europe early in the 13th Century, which soon made the Roman numeral system obsolete, and opened the way for great advances in European mathematics.
  22. 22. Throughout the 19th century mathematics became increasingly abstract. In the 19th century lived Carl Friedrich Gauss (1777–1855). Leaving aside his many contributions to science, in pure mathematics he did revolutionary work on functions of complex variables, in geometry, and on the convergence of series. He gave the first satisfactory proofs of the fundamental theorem of algebra and of the quadratic reciprocity law.
  23. 23. This century saw the development of the two forms of nonEuclidean geometry, where the parallel postulate of Euclidean geometry no longer holds. The Russian mathematician Nikolai Ivanovich Lobachevsky and his rival, the Hungarian mathematician János Bolyai, independently defined and studied hyperbolic geometry, where uniqueness of parallels no longer holds. In this geometry the sum of angles in a triangle add up to less than 180°. Riemann also developed Riemannian geometry, which unifies and vastly generalizes the three types of geometry, and he defined the concept of a manifold, which generalizes the ideas of curves and surfaces. The 19th century saw the beginning of a great deal of abstract algebra. Hermann Grassmann in Germany gave a first version of vector spaces, William Rowan Hamilton in Ireland developed noncommutative algebra. The British mathematician George Boole devised an algebra that soon evolved into what is now called Boolean algebra, in which the only numbers were 0 and 1. Boolean algebra is the starting point of mathematical logic and has important applications in computer science.
  24. 24. The 19th century saw the founding of a number of national mathematical societies: the London Mathematical Society in 1865, the Société Mathématique de France in 1872, the Circolo Matematico di Palermo in 1884, the Edinburgh Mathematical Society in 1883, and the American Mathematical Society in 1888. The first international, special-interest society, the Quaternion Society, was formed in 1899, in the context of a vector controversy. In 1897, Hensel introduced p-adic numbers.
  25. 25. The 20th century saw mathematics become a major profession. Every year, thousands of new Ph.D.s in mathematics were awarded, and jobs were available in both teaching and industry. An effort to catalogue the areas and applications of mathematics was undertaken in Klein's encyclopedia. In a 1900 speech to the International Congress of Mathematicians, David Hilbert set out a list of 23 unsolved problems in mathematics. These problems, spanning many areas of mathematics, formed a central focus for much of 20thcentury mathematics. Today, 10 have been solved, 7 are partially solved, and 2 are still open. The remaining 4 are too loosely formulated to be stated as solved or not.
  26. 26. Differential geometry came into its own when Einstein used it in general relativity. Entire new areas of mathematics such as mathematical logic,topology, and John von Neumann's game theory changed the kinds of questions that could be answered by mathematical methods. All kinds ofstructures were abstracted using axioms and given names like metric spaces, topological spaces etc. As mathematicians do, the concept of an abstract structure was itself abstracted and led to category theory. Grothendieck and Serre recast algebraic geometry using sheaf theory. Large advances were made in the qualitative study of dynamical systems that Poincaré had begun in the 1890s. Measure theory was developed in the late 19th and early 20th centuries. Applications of measures include the Lebesgue integral, Kolmogorov's axiomatisation of probability theory, and ergodic theory. Knot theory greatly expanded. Quantum mechanics led to the development of functional analysis. Other new areas include, Laurent Schwartz'sdistribution theory, fixed point theory, singularity theory and René Thom's catastrophe theory, model theory, and Mandelbrot's fractals. Lie theory with its Lie groups and Lie algebras became one of the major areas of study.
  27. 27. One of the more colorful figures in 20th-century mathematics was Srinivasa Aiyangar Ramanujan (1887–1920), an Indian autodidact who conjectured or proved over 3000 theorems, including properties of highly composite numbers, the partition function and its asymptotics, and mock theta functions. He also made major investigations in the areas of gamma functions, modular forms, divergent series, hypergeometric series and prime number theory. Paul Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. Mathematicians have a game equivalent to the Kevin Bacon Game, which leads to the Erdős number of a mathematician. This describes the "collaborative distance" between a person and Paul Erdős, as measured by joint authorship of mathematical papers.
  28. 28. In 2000, the Clay Mathematics Institute announced the seven Millennium Prize Problems, and in 2003 the Poincaré conjecture was solved by Grigori Perelman (who declined to accept an award on this point). Most mathematical journals now have online versions as well as print versions, and many online-only journals are launched. There is an increasing drive towards open access publishing, first popularized by the arXiv.
  29. 29. Mathematics is creative. Mathematics is exciting and multifaceted. Mathematics is the future. Without mathematics, modern key technologies would be unimaginable. In fact, without mathematics, the entire universe would most likely remain a complete mystery to us.
  30. 30. Many mathematicians have been expecting a great rise of the mathematical inventions in future.A lot assumtions have been taken till now. Many have been trying to create a pyramid using the theorems like that of Pythagoras .
  31. 31. Also many expect to create a formula as to drive rockets to such a speed which can even cross the universe. The army forces of many nations are trying to create a helicopter using formula of euler.
  32. 32.  Many applications of exploring trigonometric identities have been done and many more are in progress. Also using the knowledge of volumes and areas of objects like FRUSTUM ,CONE,CUBOIDetc many more styles ,shapes and textures are expected to be founded.
  33. 33. Nasa also expects to create a telescope as to see more than distance of 10 billion kilometers! The flying car i.e. the one which has a air cusion has been invented using maths. Also more and more super computers are being created using maths
  34. 34. These kind of supercomputers can do calculations in around 12.3 seconds Which humans can do in around 1 million years !! Also many new chapters and theorems can be invented.
  35. 35. Childhood And Early Life Euclid of ‘Alexandria’ was born around 330 B.C, presumably at Alexandria. Certain Arabian authors assume that Euclid was born to a wealthy family to ‘Naucrates’. It is said that Euclid was possibly born in Tyre and lived the rest of his life in Damascus. There have been certain documents that suggest that Euclid studied in Plato’s ancient school in Athens, where only the opulent studied. He later shifted to Alexandria in Egypt, where he discovered a well-known division of mathematics, known as ‘geometry’. The life of Euclid of Meguro has often been confused with the life of Euclid of Alexandria, making it difficult to believe any trustworthy information based on the life of the mathematician. He inculcated an interest in the field of mathematics and took the subject to a whole new level with path breaking discoveries and theorems. Alexandria was once, the largest city in the Western World and was also central to the great, flourishing, Papyrus industry. It was in this city where Euclid developed, imparted, and shared his knowledge on mathematics and geometry with the rest of the world.
  36. 36. Works & Achievements: He was responsible in connoting Geometrical knowledge and also wrote the famous Euclid's Elements and framed the skeleton for geometry that would be used in mathematics by the Western World for over 2000 years. Although little is known about Euclid's early and personal life, he was known as the forerunner of geometrical knowledge and went on to contribute greatly in the field of mathematics. Also known as the 'father of Geometry', Euclid was known to have taught the subject of mathematics in Ancient Egypt during the reign of Ptolemy I. He was well-known, having written the most permanent mathematical works of all time, known as the 'Elements' that comprised of the 13 gigantic volumes filled with geometrical theories and knowledge.
  37. 37. Axioms Euclid stated that axioms were statements that were just believed to be true, but he realized that by blindly following statements, there would be no point in devising mathematical theories and formulae. He realized that even axioms had to be backed with solid proofs. Therefore, he started to develop logical evidences that would testify his axioms and theorems in geometry. In order to further understand these axioms, he divided them into groups of two called ‘postulates’. One group would be called the ‘common notions’ which were agreed statements of science. His second set of postulates was synonymous with geometry.
  38. 38. Childhood And Early Life Euler was born on April 15, 1707, in Basel, Switzerland. His father Paul Euler was a pastor of the Reformed Church. His mother, Marguerite Brucker was a pastor's daughter. Euler had two younger sisters - Anna Maria and Maria Magdalena. Soon after Euler was born, his family relocated to the town of Riehen. Euler’s father was a friend of Johann Bernoulli, who was a renowned European mathematician and had a great influence on Euler. At thirteen, Euler entered the University of Basel and received his Master of Philosophy in 1723. He prepared a thesis that compared the philosophies of Newton and Descartes.
  39. 39. Contributions To Mathematics Mathematical Notation Among his diverse works, the most notable was the introduction of the concept of functions. Euler also pioneered in writing f(x) to signify the function ‘f’ applied to the argument ‘x’. He also defined the contemporary notation for the trigonometric functions, the letter ‘e’, for the base of the natural logarithm (known as Euler's number), the Greek letter ‘Σ' for summations and the letter ‘i’ to signify the imaginary unit. Analysis Euler defined the use of the exponential functions and logarithms in analytic proofs. He discovered ways to state various logarithmic functions using power series, and he effectively defined logarithms for negative and complex numbers. Through these accomplishments, he enlarged the scope of mathematical applications of logarithms to a great extent.
  40. 40. Number Theory Euler proved Fermat's little theorem, Newton's identities, Fermat's theorem on sums of two squares, and he also distinctively contributed to Lagrange's foursquare theorem. He supplied significant value addition to the theory of perfect numbers, which had always been a captivating topic for several mathematicians.
  41. 41. LEONHARD EULER TIMELINE 1707:Was born on April 15, in Basel, Switzerland 1723:Received his Master of Philosophy with a thesis that compared the philosophies of Descartes and Newton. 1726:Finished a dissertation on the propagation of sound titled ‘De Sono’. 1727:Entered the Paris Academy Prize Problem competition and won second place. 1731:Was made a professor of physics. 1734:On 7 January, he married Katharina Gsell. 1735:Became almost blind in his right eye. 1741:Left St. Petersburg on 19 June to take up a post at the Berlin Academy. 1748:Published the ‘Introductio in analysin infinitorum’, a manuscript on functions. 1783:Suffered a brain hemorrhage and died a few hours later in Saint Petersburg. 1785:The Russian Academy of Sciences placed a marble bust of Leonhard Euler on a pedestal next to the Director's seat. 1837:The Russian Academy of Sciences placed a headstone on Euler's grave.
  42. 42. Pythagoras Childhood And Early Life Pythagoras was born in the island of Samos in around 569 BC. His father, Mnesarchus, was a merchant and his mother Pythais, was a native of Samos. Young Pythagoras spent most of his early years in Samos but travelled to many places with his father. He was intelligent, welleducated. Pythagoras was also fond of poetry and recited the poems of Homer.
  43. 43. Mathematical Concepts Pythagoras studied properties of numbers and classified them as even numbers, odd numbers, triangular numbers and perfect numbers etc. The ‘Pythagoras theorem’ is one of the earliest theorems in geometry, which states that in right-angle triangles, the square of the hypotenuse is equal to the sum of square the other two sides. This theorem was already proposed during the reign of the Babylonian King Hammurabi, but Pythagoras applied it to mathematics and science and refined the concept. Pythagoras also asserted that dynamics of the structure of the universe lies on the interaction of the contraries or the opposites, such as, light and darkness, limited and unlimited, square and oblong, straight and crooked, right and left, singularity and plurality, male and female, motionless and movement and good and bad.
  44. 44. PYTHAGORAS TIMELINE 570 BC:Pythagoras was born in Samos, Greece. 535 BC:He left Samos and travelled to Egypt when Polycrates took control over Samos. 525 BC:He was made prisoner by the King of Persia and was taken to Babylon. 520 BC:Obtained freedom and returned to Samos. 518 BC:Travelled to Italy. 495 BC:Pythagoras died in Metapontum, Italy.
  45. 45. Early Life Srinivasa Ramanujan was born at his grandmother’s house in Erode, a small town located about 400 km towards southwest Madras. His father was a clerk in a textile shop in Kumbakonam. Young Ramanujan contracted small pox in 1889 December. However, unlike many other people in that town, Ramanujan overcame the epidemic invasion even thoughhis family his father’s income was barely sufficient to meet extra medical expenses. When he was five, he was sent to a primary school in Kumbakonam. Before he entered the Town High school in Kumbakonam in 1898 January, he went to several other private schools. While in school, he excelled in all the subjects and was considered as an all-rounder. Towards 1900, he began to work towards developing his mathematical ability, dealing with geometrics and arithmetic series. His talent was exposed to the world very early in 1902, when he showed how to solve cubic equations and also sought a method to solve quartic. While in Town High School, he read a book ‘Synopsis of elementary results in mathematics’, which was very concise that he could teach himself without taking help from any tutor. In this book, various theorems were mentioned in the book, along with shortcuts and formulas to solve them. During this time, Ramanujan engaged himself in deep research in 1904 and during this time he investigated the series ‘sigma 1/n’ and also extended Euler’s constant to 15 decimal points. Because of his great work in school studies, he was awarded a scholarship to attend Government College in Kumbakonam, in 1904
  46. 46. Ramanujan-Hardy Number (1729) When Ramanujan fell ill, Hardy came to his residence to visit Ramanujan in a cab with a number 1729. That day, he made a comment to Ramanujan saying that the number appeared to be very dull number. Ramanujan corrected him instantly saying that is an interesting number and explained that it is the smallest natural number that could be expressed as the sum of two positive cubes, in two different ways (i.e., 13 + 123 and 93 + 103.)
  47. 47. SRINIVASA RAMANUJAN TIMELINE 1887: Srinivasa Ramanujan was born in Erode on 22 December. 1889: He contracted small pox and fortunately, recovered from the infection. 1898: He entered the Town High School in Kumbakonam. 1900: He began developing his mathematical ability by dealing with geometrics and arithmetic series. 1902: He showed how to solve cubic equations and also sought a method to solve quartic. 1914: He went to London 1916: 16 March, he graduated from Cambridge and acquired a degree, Bachelor of Science by Research. 1919: He went back to India. 1920: He passed away on 26 April.
  48. 48. Aryabhatta is the first of the great astronomers of the classical age of India. He was born in Kerala, South India in 476 AD but later lived in Kusumapura, which his commentator Bhaskara I (629 AD) identifies with pataliputra (modern Patna) in Bihar. His first name “Arya” is hardly a south Indian name while “Bhatt” (or Bhatta) is a typical north Indian name even found today specially among the trader community.
  49. 49. Aryabhatta was the first to explain how the Lunar Eclipse and the Solar Eclipse happened. Aryabhatta also gave close approximation for Pi. In the Aryabhatiya, he wrote-“Add 4 to 100, multiply by 8, then add 62000 and then divided by 20000. The result is approximately the circumference of a circle of diameter twenty thousand. By this rule the relation of the circumference to diameter is given.” In other words, p ~ 62832/20000= 3.1416, correct to four rounded – off decimal places. Aryabhatta was the first astronomers to make an attempt at measuring the earth’s circumference. Aryabhata accurately calculated the earth’s circumference as 24835 miles, which was only 0.2 % smaller than the actual value of 24,902 miles. This approximation remained the most accurate for over a thousand years.

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